From Euler's formula, the real-part of these eigenfunctions are exponentially-decaying sinusoids:

From the above equation, it can be re-arranged to show that

From the Shockley ideal diode equation given above, it might appear that the voltage has a positive temperature coefficient ( at a constant current ), but usually the variation of the reverse saturation current term is more significant than the variation in the thermal voltage term.

From the equation for density ( ρ = m / V ), mass density must have units of a unit of mass per unit of volume.

From a mathematical viewpoint, continuous-time IIR LTI filters may be described in terms of linear differential equations, and their impulse responses considered as Green's functions of the equation.

From equation ( ii ) it is a clear that degree of ionization increases on dilution.

From the agenda points of the conference Drake derived the Drake equation by multiplying the various factors that were discussed at the conference.

From the Arrhenius equation, the activation energy can be expressed as

From the standpoint of the Fisher equation ( see above ), there was a concomitant drop both in money supply ( credit ) and the velocity of money which was so profound that price deflation took hold despite the increases in money supply spurred by the Federal Reserve.

From the equation, we see a speed – accuracy trade off associated with pointing, whereby targets that are smaller and / or further away require more time to acquire.

: From Schrödinger's equation to quantum search algorithm, American Journal of Physics, 69 ( 7 ): 769-777, 2001.

From this we find an equation for the function f ( N )

From the period and the measured distance between the pivots, the acceleration of gravity can be calculated with great precision from the periodicity equation for a simple pendulum, ( 1 ) below.

From the last equation, we can deduce Goldbach's theorem ( named after Christian Goldbach ): no two Fermat numbers share a common factor.

From analyzing equation 6 it is evident that the Otto cycle efficiency depends directly upon the compression ratio.

From here, it is easy to isolate the mass that would satisfy this equation in our system of units:

From the equation above, noise power in a resistor at room temperature, in dBm, is then:

From the previous equation, it can be deduced that the observed image depends not only on the amplitude of beam, but also on the phase of the electrons, although phase effects may often be ignored at lower magnifications.

The above steps give the N backward vectors for M. From there, a more arbitrary equation is:

From the equation we can see that the markup and the price elasticity of demand are inversely related, as the demand becomes more elastic the markup becomes smaller.

From the Schrödinger equation, the phase of an eigenfunction with energy E goes as.

From this equation, we obtain:

From this results the Heisenberg equation of motion:

From this equation, we'll show how infinite uniform plane waves comprise one field solution ( out of many possible ) in free space.

From this they created a differential equation for the shape of the bundle relating the elasticity, gravity, and orientational disorder and extracted a simple equation of state to relate the swelling pressure to the measured random curvatures of individual hairs.

From the equilibrium sorption data which are available, it seems logical to expect that polyphosphate ions would be strongly sorbed on the surface of the dirt ( especially clay soils ) so as to give it a greatly increased negative charge.

From the eigenvalues and the eigenvectors of A it is possible to determine if an initial point will converge or diverge to the equilibrium point at the origin.

From this time on, this lizard became the symbol of Nature ’ s delicate equilibrium in the Eolian Islands.

From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and explains the phenomenon of irreversibility in nature.

From a public economics perspective, subsidies of any kind work to create a socially and politically acceptable equilibrium that is not necessarily Pareto Efficient.

From Geddes ' perspective, the purpose of his theory and understanding of relationships among the units of society was to find an equilibrium among people and the environment to improve such conditions.

From static equilibrium of an infinitesimal material element at ( Figure 8. 2 ), the normal stress and the shear stress on any plane perpendicular to the-plane passing through with a unit vector making an angle of with the horizontal, i. e. is the direction cosine in the direction, is given by:

From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium — a warm gas.

From this energy difference, the equilibrium constant for the two conformations can be determined.

From these association (' on rate ', ) and dissociation rates (' off rate ', ), the equilibrium dissociation constant (' binding constant ', ) can be calculated.

From the statistical point of view, β is a numerical quantity relating two macroscopic systems in equilibrium.

From the comparison of formulae ( 2 ) and ( 3 ), both of which express the same real solar motion in the same real time but on different time scales, Clemence arrived at an explicit expression, estimating the difference in seconds of time between ephemeris time and mean solar time, in the sense ( ET-UT ):

In the mean time the World Bank loan Haiti US $ 200 Million to rebuild RN2, From River Froide which was where the starting point of RN2 all the way to Aquin and Repair on RN1 from Titanyen to Cap-Haitian.

From the steamboat's cabin Kurtz was placed in, he is heard yelling at the manager: "' Save me !— save the ivory, you mean.

* From Rumon or Rumen, archaic name of the Tiber, which in turn has the same root as the Greek verb ῥέω ( rhèo ) and the Latin verb ruo, which both mean " flow ";

In the book From Religion to Philosophy, Francis Cornford suggests that the Orphics used the word " theory " to mean ' passionate sympathetic contemplation '.

From mid-January to mid-February 1945, the mean point of V-2 impacts edged eastward at the rate of a couple of miles a week, with more and more V-2s falling short of central London.

From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.

: From what I can gather it seems that the Ancient Mariner has upon the whole been an injury to the volume, I mean that the old words and the strangeness of it have deterred readers from going on.

The film publication Cineaste published a review of The Italian in March 2009, focusing on the film's depiction of the Italian-American immmigrant experience as a Darwinian jungle rather than a promised land paved with gold :" Against Horatio Alger expectations, The Italian is a story of failure suffused with a soft-focused, dappled nostalgia for the old country ... ' From sunny Italy to the New York ghetto ,' read the taglines on Paramount's original one-sheet, contrasting scenes of ' carefree Beppo at home ' in the serene canals of Old Italy with the mean streets of New York where ' to live your baby must have Pasteurized milk.

From the seventh century the dominant power in Ulster were the Dál Fiatach so much so that the title " Rí Uladh " could simultaneously mean " King of Ulster " and " King of the Dál Fiatach ".

From the beginning of the Zhou dynasty in 1045 BC to the time of the First Emperor, rulers of the Chinese states were titled Wang (), a term that originally meant " big man " but later came to mean " chief " or " king ".

From Painshill Park the river flows northwestwards towards the Thames, passing West End Common and at Esher the mean flow of the river is.

From baseline to termination, the percentage above the cutoff score for dependent personality disorder improved significantly ( 21 % versus 8 %) as did the mean number of dependent personality disorder criteria met by the whole sample ( 3. 3 versus 2. 3 ).

From this simple intuition it is already clear that domains often do not have a greatest element, since this would mean that there is an element that contains the information of all other elements-a rather uninteresting situation.

Bruno's publicist throughout most of his career was sports historian Norman Giller, who wrote three books in harness with Frank: Know What I mean, Eye of the Tiger and From Zero to Hero.

Knowing then, brethren, of what kind of heresy was Marcion ... From others who used this very gospel — I mean from the successors of those who started it, whom we call Docetae, for most of its ideas are of their school — from them, I say, I borrowed it, and was able to go through it, and to find that most of it belonged to the right teaching of the Saviour, but some things were additions.

From the 17th century to the late 19th century, planetary ephemerides were calculated using time scales based on the Earth's rotation: usually the mean solar time of one of the principal observatories, such as Paris or Greenwich.

From 1953 to 1991, the mean daily low was 73. 6 ° F and the mean daily high was 88. 1 ° F, with April being warmest and January coolest.

From these results, lists are known of all harmonic divisor numbers up to 2 × 10 < sup > 9 </ sup >, and all harmonic divisor numbers for which the harmonic mean of the divisors is at most 300.

From " kings ", tian was semantically extended to mean " dead kings ; ancestral kings ", who controlled " fate ; providence ", and ultimately a single omnipotent deity Tian " Heaven ".

From this it was a natural extension to mean cooked vegetables or even fish and vegetables cooked together.

From the human subjective point of view, attributes may appear to posit differences in God ; but this does not mean that they do so in God objectively.

From the beginning the military establishment rightly understood that the breakup of the all-black unit would in a closed society necessarily mean more than mere desegregation.